math help

What is 40/41 + 4/6?

What is 40/41 + 4/6?

Here's how to add

40
41
 +
4
6

Step 1

Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.

So, we multiply 40 by 6, and get 240, then we multiply 41 by 6 and get 246.

40/41 times 6

Now for the second term. You multiply 4 by 41, and get 164, then multiply 41 by 6 and get 246.

4/6 times 41

We now have a new problem, that looks like this:

240
246
 +
164
246

Step 2

Since our denominators match, we can add the numerators.

240 + 164 = 404

Answer:

404
246

Step 3

Now, do we need to simplify this fraction?

First, we attempt to divide it by 2...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

404
246
 ÷ 2 =
202
123

Now, try the same number again.

Nope. Try the next prime number, 3...

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

Nope. Try the next prime number, 41...

Nope. Try the next prime number, 43...

Nope. Try the next prime number, 47...

Nope. Try the next prime number, 53...

Nope. Try the next prime number, 59...

Nope. Try the next prime number, 61...

Nope. Try the next prime number, 67...

Nope. Try the next prime number, 71...

Nope. Try the next prime number, 73...

Nope. Try the next prime number, 79...

Nope. Try the next prime number, 83...

Nope. Try the next prime number, 89...

Nope. Try the next prime number, 97...

Nope. Try the next prime number, 101...

Nope. Try the next prime number, 103...

Nope. Try the next prime number, 107...

Nope. Try the next prime number, 109...

Nope. Try the next prime number, 113...

Nope. Try the next prime number, 127...

No good. 127 is larger than 123. So we're done reducing.

Congratulations! Here's your final answer to 40/41 + 4/6

40
41
 +
4
6
 =
202
123
© 2014 Randy Tayler

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